Geodesic
Boubaker hybrid functions and their application to solve fractional optimal control and fractional variational problems
Applications of Mathematics, Tome 63 (2018) no. 5, pp. 541-567.

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A new hybrid of block-pulse functions and Boubaker polynomials is constructed to solve the inequality constrained fractional optimal control problems (FOCPs) with quadratic performance index and fractional variational problems (FVPs). First, the general formulation of the Riemann-Liouville integral operator for Boubaker hybrid function is presented for the first time. Then it is applied to reduce the problems to optimization problems, which can be solved by the existing method. In this way we find the extremum value of FOCPs without adding slack variables to inequality trajectories. Also we show that if the number of bases is increased, the used approximations in this method are convergent. The applicability and validity of the method are shown by numerical results of some examples, moreover, a comparison with the existing results shows the preference of this method.
DOI : 10.21136/AM.2018.0083-18
Classification : 49J15, 49J40
Keywords: fractional optimal control problems; fractional variational problems; Riemann-Liouville fractional integration; hybrid functions; Boubaker polynomials; Laplace transform; convergence analysis 
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     title = {Boubaker hybrid functions and their application to solve fractional optimal control and fractional variational problems},
     journal = {Applications of Mathematics},
     pages = {541--567},
     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2018.0083-18/}
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Rabiei, Kobra; Ordokhani, Yadollah. Boubaker hybrid functions and their application to solve fractional optimal control and fractional variational problems. Applications of Mathematics, Tome 63 (2018) no. 5, pp. 541-567. doi : 10.21136/AM.2018.0083-18. http://geodesic.mathdoc.fr/articles/10.21136/AM.2018.0083-18/

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